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MC-CIG - Support for training and career development of researcher (CIG)

Cel

The work we propose focuses on the rigorous mathematical development of kinetic theory and the applications of its techniques to the study of models of population dynamics and cell fragmentation and growth in biology, to the dynamics of coagulation and fragmentation processes in physics, and to more recently developed models in the field of collective behavior. The aim is then twofold: to advance the understanding of basic equations in kinetic theory, such as the Boltzmann equation, and to employ known or newly developed techniques in this field to the rigorous treatment of models in the above mentioned areas, such as the Becker-Döring equation for nucleation, the growth-fragmentation model for cell populations, or individual-based models for collective behavior.

The proposed work on the Boltzmann equation is a continuation of previous works of the applicant in collaboration with M. Bisi, B. Lods and C. Mouhot, mainly based on perturbation and entropy techniques in the study of asymptotic behavior of the elastic or inelastic Boltzmann equation.The work on applications builds on recent advances showing the successful applicability of techniques form kinetic theory in some models involving coagulation and fragmentation. In particular, we expect to obtain improved results on the asymptotic behavior of the growth-fragmentation equation, including the development and analysis of computer code to calculate the asymptotic profile; to apply entropy techniques to the full coagulation-fragmentation equation in order to study its speed of convergence to equilibrium; and to be able to apply perturbation techniques in the study of the scaling hypothesis for coagulation.